Ultra-precision positioning system

ABSTRACT

Provided is an ultra-precision positioning system. The system comprises a base, a motion stage movably provided to the top of the base, and first to sixth feeding mechanisms for moving the motion stage to have six degrees of freedom. The first to sixth feed mechanisms are fixed to the base and the motion stage, respectively. Each of the first to third feeding mechanisms has a piezo actuator and two elastic hinges provided at both sides of the piezo actuator. Each of the fourth to sixth feeding mechanisms has a piezo actuator, three hinge members, and a lever member with a notch hinge which operatively cooperates with the hinge members.

TECHNICAL FIELD

The present invention relates to an ultra-precision positioning system,and more particularly, to an ultra-precision positioning system capableof precisely performing a multi-degree-of-freedom fine motion of thesubmicron order.

BACKGROUND ART

As well known, the importance of ultra-precision positioning technologyhas gradually increased in a variety of industrial fields. Inparticular, the development of semiconductor technology results in highintegration of circuits. Consequently, a line width for use in thelatest microprocessor is in the order of 0.18 μm which is 1/500 times aslarge as the diameter of a hair. In such a case, the accuracy requiredfor a wafer manufacturing stage should meet reproducibility requirementsof 20 nm that is 1/10 times as large as the line width. Further, anultra-precision feeding apparatus implemented in the submicron order canbe utilized in ultra-precision measurement fields, such as an atomicforce microscope (AFM) and a scanning electron microscope (SEM), and inindustrial fields including the information industry, and thus, it has awide range of application.

A general positioning apparatus using a linear motor, or a servomotorand a ball screw has a relatively long stroke. However, it has alimitation on implementable positional accuracy due to a structurallimitation such as backlash. The general positioning apparatus also hasa disadvantage in that the height of the entire system is increasedsince an actuator is arranged vertically to obtain a vertical motion.This leads to many difficulties in controlling a vertical position inworks requiring high accuracy.

Meanwhile, the ultra-precision positioning apparatus for achieving amotion of submicron order should be designed in such a manner that thereis no frictional portion to eliminate or minimize nonlinear factors.Further, in the ultra-precision positioning apparatus, the actuatoritself should be constructed by a component that can be easily driven inthe submicron order and has high repeatability. Moreover, it isnecessary to design the ultra-precision positioning apparatus so thatits height can be kept as low as possible.

DISCLOSURE OF INVENTION

The present invention is conceived to solve the aforementioned problemsin the prior art. An object of the present invention is to provide anultra-precision positioning system capable of precisely performing amulti-degree-of-freedom fine motion of the submicron order.

Another object of the present invention is to provide an ultra-precisionpositioning system, wherein there is no interference wear and very highrepeatability can be maintained, thanks to hinge structures havingelasticity.

A further object of the present invention is to provide anultra-precision positioning system capable of performing a continuousand smooth fine motion.

A still further object of the present invention is to provide anultra-precision positioning system capable of making the entire heightthereof low and enhancing the stiffness of a motion stage itself.

A still further object of the present invention is to provide anultra-precision positioning system which is little influenced by achange or gradient of temperature.

In order to achieve the above objects, an ultra-precision positioningsystem according to the present invention comprises a base; a motionstage movably provided above a top of the base; a first feeding meansincluding a first actuator and first and second hinge elements with acircular hinge, the first feeding means performing an x-axistranslational motion of the motion stage with respect to the base; asecond feeding means including a second actuator and first and secondhinge elements with a circular hinge, the second feeding meansperforming a y-axis translational motion and a z-axis rotational motionof the motion stage with respect to the base; a third feeding meansincluding a third actuator and first and second hinge elements with acircular hinge, the third feeding means performing the y-axistranslational motion and the z-axis rotational motion of the motionstage with respect to the base in cooperation with the second feedingmeans; a fourth feeding means including a fourth actuator, first andsecond hinge members with a circular hinge, a first lever membercooperating with the second hinge member, and a third hinge membercooperating with the first hinge member, the fourth feeding meansperforming an x-axis rotational motion of the motion stage with respectto the base; and a control means for controlling the first to fourthactuators of the first to fourth feeding means.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a perspective view schematically showing the entireconstitution of an ultra-precision positioning system according to thepresent invention;

FIG. 2 is a plan view of the ultra-precision positioning systemaccording to the present invention;

FIG. 3 is a plan view showing the constitutions of a base and first tosixth feeding mechanisms of the ultra-precision positioning systemaccording to the present invention in a state where a motion stage isremoved therefrom;

FIG. 4 is a block diagram illustrating a control means of theultra-precision positioning system according to the present invention;

FIG. 5 is a perspective view showing the constitution of the base of theultra-precision positioning system according to the present invention;

FIGS. 6 a and 6 b are a perspective view and an exploded perspectiveview showing the constitution of the first feeding mechanism accordingto the present invention;

FIGS. 7 a and 7 b are a perspective view and an exploded perspectiveview showing the constitution of the fourth feeding mechanism accordingto the present invention;

FIG. 8 is a partial front view illustrating the constitution of acircular hinge in the ultra-precision positioning system according tothe present invention;

FIG. 9 is a view illustrating a model for obtaining a distance betweenthe second and third feeding mechanisms according to the presentinvention; and

FIGS. 10 a and 10 b are sectional views showing an operation of thefourth feeding mechanism according to the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, a preferred embodiment of an ultra-precision positioningsystem according to the present invention will be described in detailwith reference to the accompanying drawings.

Referring first to FIGS. 1 and 3, an ultra-precision positioning systemaccording to the present invention comprises a stationary base 10, amotion stage 20 which is provided above a top of the base 10 and makes asix-degree-of-freedom motion with respect to the base 10, first to sixthfeeding mechanism 30, 40, 50, 60, 70 and 80 for performing thesix-degree-of-freedom motion of the motion stage 20 with respect to thebase 10. The first feeding mechanism 30 performs an x-axis translationalmotion of the motion stage 20 with respect to the base 10, as shown inFIG. 1. The second and third feeding mechanisms 40, 50 cooperate witheach other and perform a y-axis translational motion and a z-axisrotational motion of the motion stage 20 with respect to the base 10.The fourth to sixth feeding mechanisms 60, 70 and 80 cooperate with oneanother and perform a z-axis translational motion, an x-axis rotationalmotion and a y-axis rotational motion of the motion stage 20 withrespect to the base 10.

Referring to FIG. 3, the first to third feeding mechanisms 30, 40 and 50comprise first to third piezo actuators 31, 41 and 51, and first hingeelements 32, 42 and 52 with circular hinges 32 a, 42 a and 52 a andsecond hinge elements 33, 43 and 53 with circular hinges 33 a, 43 a and53 a to constitute stage driving parts. The first hinge elements 32, 42,and 52 and the second hinge elements 33, 43, and 53 are fixedly arrangedto both ends of each of the first to third piezo actuators 31, 41 and51. The fourth to sixth feeding mechanisms 60, 70 and 80 comprise fourthto sixth piezo actuators 61, 71 and 81, and first, fourth and seventhhinge members 62, 72 and 82 with circular hinges 62 a, 72 a and 82 a,and second, fifth and eighth hinge members 63, 73 and 83 with circularhinges 63 a, 73 a and 83 a to constitute stage driving parts. The first,fourth and seventh hinge members 62, 72 and 82 and the second, fifth andeighth hinge members 63, 73 and 83 are fixedly arranged to both ends ofeach of the fourth to sixth piezo actuators 61, 71 and 81 and constitutestage driving parts, respectively. The fourth to sixth feedingmechanisms 60, 70 and 80 further comprise third, sixth and eighth hingemembers 67, 77 and 87; and first, second and third lever members 68, 78and 88, respectively. The circular hinges are elastic hinges which havea linear relationship between force and displacement and make adeformable motion using elastic deformation of the material itself ofthe hinges. Further, since the circular hinges have no relative motionsat contact surfaces, their driving by fine displacement is madecontinuous and a smooth motion locus is provided. Moreover, sincefracture mechanism due to fatigue or excessive force can be easilyexpected in brittle material, a hinge structure made of elastic-brittlematerial can be easily applied to a system having very highrepeatability. Although the present embodiment utilizes the piezoactuator, it may employ a voice coil actuator or a magnetic actuatorinstead of the piezo actuator.

The first feeding mechanism 30 is aligned with an x-axis centerline ofthe base 10, and a center of the hinge 33 a of the second hinge element33 of the first feeding mechanism 30 which is positioned on a side to befixed to the motion stage 20 is coincident with the center of the motionstage 20. FIG. 3 clearly shows that the center of the hinge 33 a of thefirst feeding mechanism 30 is coincident with an intersecting point ofthe x-axis centerline and a y-axis centerline which is the center of thebase 10 or the motion stage 20. The second and third feeding mechanisms40, 50 are arranged parallel to a y-axis centerline of the base 10, andthe hinges 43 a, 53 a of the second hinge elements 43, 53 of the secondand third feeding mechanisms 40, 50 lie on the x-axis centerline, asshown in FIG. 3. The fourth feeding mechanism 60 is arranged above andparallel to the x-axis centerline of the base 10, and the hinge 63 a ofthe fourth feeding mechanism 60 which is positioned on a side to befixed to the motion stage 20 lies on the y-axis centerline of the base10. The fifth and sixth feeding mechanisms 70, 80 are arranged below andparallel to the x-axis centerline of the base 10 and to be symmetricwith each other with respect to the y-axis centerline. The fourthfeeding mechanism 60 and the fifth and sixth feeding mechanisms 70, 80are installed to be spaced apart by a predetermined interval D (seeFIG. 1) from each other, as will be described later.

FIG. 4 shows a block diagram of control of the ultra-precisionpositioning system according to the present invention. Referring to FIG.4, in order to perform an ultra-precision motion of the motion stage 20,the ultra-precision positioning system according to the presentinvention comprises a controller 90 for outputting and controllingdriving signals for use in drive of the first to sixth piezo actuators31, 41, 51, 61, 71 and 81; first to sixth amplifiers 91 a to 91 f foramplifying the driving signals from the controller 90 and inputting theamplified signals into the first to sixth piezo actuators 31, 41, 51,61, 71 and 81, and first to sixth sensors 92 a to 92 f for detecting amotion position of the motion stage 20 moved by the first to sixthfeeding mechanisms 30, 40, 50, 60, 70 and 80. In the present embodiment,each of the first to sixth sensors 92 a to 92 f can include a mirror(not shown) attached to the top of the motion stage 20, and a laserinterferometer (not shown) having a laser for scanning the mirror with alaser beam. Further, as shown in FIGS. 2 and 3, the first to sixth piezoactuators 31, 41, 51, 61, 71 and 81 and the controller 90 areelectrically connected with one another through a cable 93.

The driving signals for the first to sixth piezo actuators 31, 41, 51,61, 71 and 81 are outputted by means of the control of the controller90. When the signals amplified by the first to sixth amplifier 91 a to91 f are inputted into the first to sixth piezo actuators 31, 41, 51,61, 71 and 81, displacement is generated in each of the first to sixthpiezo actuators 31, 41, 51, 61, 71 and 81. Each displacement generatedfrom the first to sixth piezo actuators 31, 41, 51, 61, 71 and 81 istransferred to the motion stage 20 through the aforementioned circularhinges 33 a, 43 a, 53 a, 63 a, 73 a and 83 a so that the motion stage 20is moved. The motion position of the motion stage 20 is detected by thefirst to sixth sensors 92 a to 92 f and the controller 90 corrects themotion position of the motion stage 20 based on feedback signalsinputted from the first to sixth sensors 92 a to 92 f.

As shown in FIG. 5, first to sixth installation recesses 11 a to 11 ffor allowing the first to sixth feeding mechanisms 30, 40, 50, 60, 70and 80 to be installed therein are formed in the top of the base 10, andslots 12 are formed in the first to third installation recesses 11 a to11 c, respectively.

Referring to FIGS. 3, 6 a and 6 b, threaded parts 32 b, 33 b formed ateach one end of the first and second hinge elements 32, 33 are fastenedto both the ends of the piezo actuator 31 of the first feeding mechanism30, respectively. A cylindrical fixing portion 32 c formed at the otherend of the first hinge element 32 is fixedly fitted into a hole 34 a ofa first fixing block 34. The first fixing block 34 is fitted into thefirst installation recess 11 a of the base 10 and then fixedly attachedthereto by fixing means which penetrate through the slots, for example,screws. A cylindrical fixing portion 33 c formed at the other end of thesecond hinge element 33 is fixedly fitted into a hole 35 a of a secondfixing block 35, and the second fixing block 35 is fixedly attached tothe bottom of the motion stage 20 by means of fastening of screws. Asupport plate 36 has a hole 36 a formed in a center thereof to support afixing portion 33 c of the second hinge element 33 fitted into a hole 35a of the second fixing block 35. The support plate 36 is fixedlyattached to the second fixing block 35 by means of fastening of screws36 b to prevent escape of the second hinge element 33.

In the ultra-precision positioning system according to the presentinvention, the second and third feeding mechanisms 40, 50 areconstructed in the same way as the first feeding mechanism 30.Therefore, since the constitutions and operations of the second piezoactuator 41 and first and second hinge elements 42, 43 of the secondfeeding mechanism 40 and the third piezo actuator 51 and first andsecond hinge elements 52, 53 of the third feeding mechanism 50 are thesame as the first piezo actuator 31 and first and second hinge elements32, 33 of the first feeding mechanism 30, the detailed description ofthe second and third feeding mechanisms 40, 50 will be omitted.

Referring to FIGS. 3, 7 a and 7 b, threaded parts 62 b, 63 b formed ateach one end of the first and second hinge members 62, 63 are fastenedto both the ends of the fourth piezo actuator 61 of the fourth feedingmechanism 60, respectively. A cylindrical fixing portion 62 c formed atthe other end of the first hinge member 62 is fitted into a hole 64 a ofa fixing block 64. A support plate 65 has a hole 65 a formed in a centerthereof to support a fixing portion 62 a of the first hinge member 62fitted into the hole 64 a of the fixing block 64. The support plate 65is fixedly attached to the fixing block 64 by means of fastening ofscrews 65 b to prevent escape of the first hinge member 62. Slots 64 bare formed at both sides of the fixing block 64, and pads 66 arepositioned at the tops of the slots 64 b of the fixing block 60,respectively. The fixing block 64 is fitted into one side portion of thefirst installation recess 11 d of the base 10, and screws 66 b penetratethrough the base 10 and the slots 64 b of the fixing block 64 and areengaged with threaded holes 66 a of the pads 66. Thus, the fixing block64 is fixedly attached to the base 10.

Further, a cylindrical extension 63 c is formed between the hinge 63 aand the threaded portion 63 b of the second hinge member 63 and a jointplate 63 d is formed at the other end of the second hinge member 63. Theextension 63 c of the second hinge member 63 is fitted into a hole 67 bof a body 67 a of the third hinge member 67 disposed perpendicularly tothe fourth piezo actuator 61. Upper and lower ends of the body 67 a ofthe third hinge member 67 are formed with first and second circularhinges 67 c, 67 d, respectively. First and second joint plates 67 e, 67f are connected to the first and second circular hinges 67 c, 67 d ofthe third hinge member 67, respectively. The first joint plate 67 e ofthe third hinge member 67 is fixedly attached to the bottom of themotion stage 20 by means of fastening of screws.

The fourth feeding mechanism 60 includes a first lever member 68 whichcooperates with the second hinge member 63 and the third hinge member67. The first lever member 68 comprises a first lever 68 a, a secondlever 68 b, and a notch hinge 68 c for integrally connecting the firstlever 68 a and the second lever 68 b. The first lever 68 a comprises ahorizontal portion 69 a and a vertical portion 69 b, and the secondlever 68 b is disposed to be perpendicular to the vertical portion 69 bof the first lever 68 a. The second joint plate 67 f of the third hingemember 67 is fixedly attached to the horizontal portion 69 a of thefirst lever 68 a by means of fastening of screws, while a joint plate 64d of the second hinge member 63 is fixedly attached to the verticalportion 69 b of the first lever 68 a by means of fastening of screws.The second lever 68 b of the first lever member 68 is fixedly attachedto the installation recess 11 d of the base 10 by means of fastening ofscrews.

In the ultra-precision positioning system according to the presentinvention, the fifth and sixth feeding mechanisms 70, 80 are constructedin the same way as the fourth feeding mechanism 60. Therefore, since theconstitutions and operations of the fifth piezo actuator 71, fourth tosixth hinge members 72, 73 and 77 and second lever member 78 of thefifth feeding mechanism 70 and the sixth piezo actuator 81, seventh toninth hinge members 82, 83 and 87 and third lever member 88 of the sixthfeeding mechanism 80 are the same as the fourth piezo actuator 61, firstto third hinge members 62, 63 and 67 and the first lever member 68 ofthe fourth feeding mechanism 60, the detailed description of the fifthand sixth feeding mechanisms 70, 80 will be omitted.

In the ultra-precision positioning system according to the presentinvention constructed as such, since the circular hinges are elasticallydeformed by the piezo actuators, the hinge flexure moves the motionstage while serving to limit motion directions of the motion stage orguide the motion stage in specific directions. If values of stiffness ofthe hinges are known, it is possible to find out a feed of the motionstage when forces are applied to the hinges by the piezo actuators.Assuming that an axial direction of the hinge is an x-axis, relationshipequations between the force and the displacement can be simplified likeformulas (1), (2) and (3) with respect to the x-axis and y- and z-axesthat are shear directions of the x-axis. These are well-known equationsobtained by Paros-Weisbord, which have been verified through manyexperiments.

$\begin{matrix}{\frac{\Delta\; x}{F_{x}} \approx \frac{2R^{1/2}}{{Et}^{3/2}}} & (1) \\{\frac{\Delta\; y}{F_{y}} = {\frac{\Delta\; z}{F_{z}} \approx \frac{2R^{1/2}}{{Gt}^{3/2}}}} & (2) \\{\frac{\alpha_{y}}{M_{y}} = {\frac{\alpha_{z}}{M_{z}} \approx \frac{20R^{1/2}}{{Et}^{7/2}}}} & (3)\end{matrix}$

where R and t are a radius and a thickness of the circular hinge asshown in FIG. 8, respectively, E is Young's modulus, G is a shearmodulus, M is a torsional moment, and a is a rotational angle.

Since formulas (1), (2) and (3) have values within an error range of 10%as compared with results of a finite element method, they can besufficiently accepted even through a machining tolerance of the circularhinge and hysteresis of the elastic material thereof are taken intoconsideration.

In the meantime, stress and strain to be generated in the hinge shouldbe essentially taken into consideration upon design of the hinge flexureof the present invention. In the case of design of the hinge, arelationship between angular displacement and maximum stress σ_(max) ofthe hinge is expressed as the following formula:

$\begin{matrix}{\theta = {\frac{4K}{K_{t}}\frac{R}{Et}\sigma_{\max}}} & (4)\end{matrix}$

Linear displacement can be obtained from the following formula:

$\begin{matrix}\begin{matrix}{K_{t} = {\frac{{2.7t} + {5.4R}}{{8R} + t} + 0.325}} \\{\delta = {L \cdot \theta}}\end{matrix} & (5)\end{matrix}$

where θ is the angular displacement, K is a proportional constant, K_(t)is a constant defined by formula (5), δ is feeding displacement, and Lis an effective length of the hinge. Therefore, the maximum stressσ_(max) and the Young's modulus E can be known by selecting materialsuitable for obtainment of desired displacement, and the radius R andthickness t of the hinge can be appropriately determined throughrepetitive calculations of formulas (4) and (5). The radius R andthickness t determined in such a way are substituted into formulas (1),(2) and (3) to determine the stiffness of the hinge.

In the ultra-precision positioning system according to the presentinvention, the aforementioned lever members 68, 78 and 88 are utilizedin connection with the vertical direction in order to reduce the entireheight of the system while enhancing the stiffness of the motion stageitself. If the vertical motion direction of the motion stage 20 isdefined as the z-axis, the driving system of the ultra-precisionpositioning system should have a structure of which height is low in thez-axis direction in order to minimize the height of the entireconfiguration thereof and simultaneously maximize the stiffness of thesystem. Generally, since maximum expansions of the piezo actuators 61,71 and 81 are merely about 0.1% of the lengths thereof, the piezoactuators should be long to obtain a desired feeding range. For example,in order to obtain a feed equal to or larger than 125 μm, piezoactuators having a length of 200 mm are required. Thus, according to thepresent invention, the piezo actuators 61, 71 and 81 are horizontallypositioned in consideration of the lengths thereof, and horizontalmotions of the piezo actuators are converted into vertical motions bythe lever members 68, 78 and 88, thereby reducing the height of theultra-precision positioning system according to the present invention.

The first lever member 68 will be explained by way of an example. Thelever member 68 is designed such that actual vertical displacement ofthe motion stage 20 is made to be twice as large as the horizontaldisplacement of the piezo actuator 61 by adjusting a position of thehinge 68 c which is an application point of the force transferred by thepiezo actuator 61. That is, as shown in FIG. 10 a, assuming that avertical distance between an extension line of the center of the hinge63 a of the second hinge member 63 in the x-axis direction and thecenter of the hinge 68 c of the lever member 68 is a, and a horizontaldistance between an extension line of the centers of the first andsecond hinges 67 c, 67 d of the third hinge member 67 in the y-axisdirection and the center of the hinge 68 c of the lever member 68 is b,since a central rotational angle of the hinge 68 c of the lever member68 with respect to fine displacement of the hinge 63 a of the secondhinge member 63 which is produced by the fourth piezo actuator 61 isconstant, the following formula is established:Δy[=bθ]=2Δx[=2aθ]b=2a  (6)

where θ is the rotational angle about the center of the hinge 68 c ofthe lever member 68, Δy is the vertical displacement, and Δx is thehorizontal displacement. When the horizontal displacement is produced atthe joint plate 63 d of the second hinge member 63 by the fourth piezoactuator 61, the displacement is amplified at the center of the hinge 68c of the lever member 68 according to formula (6). The amplifieddisplacement is converted into the vertical displacement by the firstlever 68 a of the lever member 68 and the second joint plate 67 f of thethird hinge member 67.

Axial stiffness K_(a) of the stage driving parts constructed by thepiezo actuators and the hinge elements and members of the presentinvention can be obtained from the following formula (7), and radialstiffness K_(r) thereof can be obtained from the following formula (8):

$\begin{matrix}{\frac{1}{K_{\alpha}} = {{2\frac{2R^{1/2}}{{Et}^{7/2}}} + \frac{1}{K_{pzt}}}} & (7) \\{\frac{1}{K_{r}} = {{\frac{L^{2}}{2}\frac{20R^{1/2}}{{Et}^{7/2}}} + \frac{2R^{1/2}}{{Gt}^{3/2}}}} & (8)\end{matrix}$

where K_(pzt) is stiffness of the piezo actutator, and L is a distancebetween the centers of the hinges of the first and second hingeelements, including the piezo actuator. The stiffness of the entirestage driving parts can be known by substituting the radius R and thethickness t into formulas (7) and (8).

Next, an operation of the ultra-precision positioning system accordingto the present invention will be described. In the following formulas,the x-axis translational motion is expressed as X, the y-axistranslation motion is expressed as Y, the z-axis translational motion isexpressed as Z, the x-axis rotational motion is expressed as Θx, they-axis rotational motion is expressed as Θy, and the z-axis rotationalmotion is expressed as Θz. Further, the driving signal for the firstpiezo actuator is expressed as X1, the driving signals for the secondand third piezo actuators are expressed as Y1 and Y2, respectively, andthe driving signals for the fourth to sixth piezo actuators areexpressed as Z1, Z2 and Z3.

First, the operation of the first feeding mechanism 30 will be describedwith reference to FIGS. 3 and 5. If the driving signal (X1) is inputtedinto the first piezo actuator 31 of the first feeding mechanism 30 underthe control of the controller 90, the x-axis translational motion of themotion stage 20 is produced as can be seen from the following formula(9):∴X=X1  (9)

At this time, the stage driving portion of the first feeding mechanism30 constructed by the first piezo actuator 31 and the first and secondhinge elements 32, 33 has axial stiffness considerably larger thanrotational stiffness thereof. Thus, the first feeding mechanism 30 cansufficiently perform alone the x-axis translational motion of the motionstage 20.

Next, the y-axis translational motion and the z-axis rotational motionof the motion stage 20 by the operations of the second and third feedingmechanisms 40, 50 will be described. If identical driving signals(Y1=Y2) are inputted into the second piezo actuator 41 of the secondfeeding mechanism 40 and the third piezo actuator 51 of the thirdfeeding mechanism 50 under the control of the controller 90, the y-axistranslational motion of the motion stage 20 is produced by the drivingof the second and third piezo actuators 41, 51, as can be seen from thefollowing formula (10):Y1=Y2∴Y=Y1(=Y2)  (10)

The z-axis rotational motion Θz of the motion stage 20 is produced whendriving signals different from each other are inputted into the secondpiezo actuator 41 of the second feeding mechanism 40 and the third piezoactuator 51 of the third feeding mechanism 50 under the control of thecontroller 90. If the distance between the second and third feedingmechanisms 40, 50 is defined as L (see FIG. 1), the value of the z-axisrotational motion Θz can be obtained from the following formula (11):Θz=(Y2−Y1)/L  (11)

In the ultra-precision positioning system according to the presentinvention, the distance L between the second and third feedingmechanisms 40, 50 should be arranged so as not to produce anyinterference between the y-axis translational motion and the z-axisrotational motion Θz. The distance L between the second and thirdfeeding mechanisms 40, 50 is determined by applying Lagrangian method orNewton's equation of motion to two variables for two directionalmotions.

If T is kinetic energy, V is potential energy, Q is an external force,and Lagrangian L=T−V, the following formula is established:

$\begin{matrix}{\frac{\alpha_{y}}{M_{y}} = {\frac{\alpha_{z}}{M_{z}} \approx \frac{20R^{1/2}}{{Et}^{7/2}}}} & (12)\end{matrix}$

Alternatively, if the Newton's equation of motion is applied, thefollowing formula is established:

$\begin{matrix}{{m\;\overset{¨}{x}} = {\sum\limits_{i}F_{i}}} & (13)\end{matrix}$

A two-degree-of-freedom equation of motion is determined in the form ofa matrix according to these formulas (12) and (13). In order tomaximally reduce interference between the two degrees of freedom, allremainder components except for diagonal components in the matrix of theequation of motion are caused to be set to 0. Accordingly, it ispossible to determine the distance L between the second and thirdfeeding mechanisms 40, 50.

Formulas (14a) to (14h) show a process of obtaining the distance Mbetween the second and third feeding mechanisms 40, 50. Referring toFIG. 9, k is a value of the stiffness obtained from formula (7), mass mand mass moment of inertia I are property values of the motion stage 20.

The equation of motion according to formula (12) or (13) can beexpressed as the following formulas:

$\begin{matrix}{{m\left( \frac{{\overset{.}{x}1} + {\overset{.}{x}2}}{2} \right)} = {{- {kx1}} - {kx2}}} & \left( {14a} \right) \\{{I\overset{¨}{\theta}} = {{- L^{2}}k\;\theta}} & \left( {14b} \right) \\{\theta = \frac{{x2} - {x1}}{L}} & \left( {14c} \right)\end{matrix}$

If formulas (14a), (14b) and (14c) are combined and arranged, thefollowing formulas are established:

$\begin{matrix}{{{\frac{m}{2}\overset{¨}{x}1} + {\frac{m}{2}\overset{¨}{x}2} + {kx1} + {kx2}} = 0} & \left( {14d} \right) \\{{{{- \frac{I}{L}}\overset{¨}{x}1} + {\frac{I}{L}\overset{¨}{x}2} - {Lkx1} + {Lkx2}} = 0} & \left( {14e} \right)\end{matrix}$

At this time, formulas (14d) and (14e) can be arranged into a matrixform of the following formula (14f):

$\begin{matrix}{{{\begin{bmatrix}\frac{Im}{L} & 0 \\0 & \frac{Im}{L}\end{bmatrix}\begin{bmatrix}{\overset{¨}{x}1} \\{\overset{¨}{x}2}\end{bmatrix}} + {\begin{bmatrix}{\frac{Ik}{L} + \frac{Lmk}{2}} & {\frac{Ik}{L} - \frac{Lmk}{2}} \\{\frac{Ik}{L} - \frac{Lmk}{2}} & {\frac{Ik}{L} + \frac{Lmk}{2}}\end{bmatrix}\begin{bmatrix}{x1} \\{x2}\end{bmatrix}}} = \begin{pmatrix}0 \\0\end{pmatrix}} & \left( {14f} \right)\end{matrix}$

In order to minimize interference between the second and third feedingmechanisms 40, 50, all remainder components except for diagonalcomponents in the matrix are caused to be set to 0. That is, if thecomponents in the 1^(st) row and 2^(nd) column and the 2^(nd) row and1^(st) column in formula (14f) satisfy the following formula (14g), thedistance L between the second and third feeding mechanisms 40, 50 isexpressed as the following formula (14h).

$\begin{matrix}{{{\frac{Ik}{L} - \frac{Lmk}{2}} = 0},} & \left( {14g} \right) \\{L = \sqrt{\frac{2I}{m}}} & \left( {14h} \right)\end{matrix}$

Finally, the operations of the fourth to sixth feeding mechanisms 60, 70and 80 will be described with reference to FIGS. 3, 4, 10 a and 10 b.The fourth to sixth feeding mechanisms 60, 70 and 80 of the presentinvention implement three degrees of freedom, i.e. the z-axistranslational motion, the x-axis rotational motion Θx and the y-axisrotational motion Θy. Therefore, the fourth to sixth feeding mechanisms60, 70 and 80 should be arranged such that any interference is notproduced among the respective motions in the same manner as the secondand third feeding mechanisms 40, 50.

Meanwhile, if identical driving signals (Z1=Z2=Z3) are inputted into thefourth to sixth piezo actuators 61, 71 and 81 of the fourth to sixthfeeding mechanisms 60, 70 and 80 under the control of the controller 90,the z-axis translational motion of the motion stage 20 is performed ascan be seen from the following formula (15):Z1=Z2=Z3∴Z=Z1(=Z2=Z3)  (15)

The y-axis rotational motion Θy of the motion stage 20 is produced whena driving signal is not inputted into the fourth piezo actuator 61 ofthe fourth feeding mechanism 60 and driving signals different from eachother are inputted into the fifth piezo actuator 71 of the fifth feedingmechanism 70 and the sixth piezo actuator 81 of the sixth feedingmechanism 80 under the control of the controller 90. That is, if thedistance between the fifth and sixth feeding mechanisms 70, 80 isdefined as d (see FIG. 1), the value of the y-axis rotational motion Θycan be obtained from the following formula (16):Θy=(Z2−Z3)/d  (16)

The x-axis rotational motion Θx of the motion stage 20 is produced whenidentical driving signals (Z2=Z3) are inputted into the fifth piezoactuator 71 of the fifth feeding mechanism 70 and the sixth piezoactuator 81 of the sixth feeding mechanism 80 and a different drivingsignal (Z1) is inputted into the fourth piezo actuator 61 of the fourthfeeding mechanism 60 under the control of the controller 90. That is, ifthe distance between the fourth feeding mechanism 60 and the fifth orsixth feeding mechanism 70 or 80 is defined as D, the value of thex-axis rotational motion Θx can be obtained from the following formula(17):Θx=(Z1−Z2)/D  (17)

Therefore, upon determination of the respective positions of the fourthto sixth feeding mechanisms 60, 70 and 80, after displacement variablescorresponding to the respective fourth to sixth feeding mechanisms 60,70 and 80 are first defined, they are determined in the form of a matrixof the equation of motion by the Lagrangian method of formula (12) orthe Newton method of formula (13) based on the kinetic and potentialenergy. In order to minimize interference among the respective degreesof freedom of the fourth to sixth feeding mechanisms 60, 70 and 80, allremainder components except for diagonal components in the matrix of theequation of motion are caused to be set to 0 in the same manner asformulas (14a) to (14 h). Accordingly, it is possible to determine thedistance D between the fourth feeding mechanism 60 and the fifth orsixth feeding mechanism 70 or 80 as well as the distance d between thefifth and sixth feeding mechanisms 70, 80.

The above description is merely the description of a preferredembodiment of the present invention and the scope of the presentinvention is not limited to the described and illustrated embodiment.Those skilled in the art can make various changes, modifications andsubstitutions thereto within the technical spirit and the scope of thepresent invention defined by the appended claims. It should beunderstood that such embodiments fall within the scope of the presentinvention.

INDUSTRIAL APPLICABILITY

According to the ultra-precision positioning system of the presentinvention mentioned above, the multi-degree-of-freedom fine motion ofthe submicron order can be precisely performed by means of the piezoactuators, the hinge elements with the circular hinges and the levermembers with the notch hinges. Furthermore, thanks to the hingestructure having elasticity, there is no interference wear and it ispossible to maintain the very high repeatability and simultaneouslyperform a continuous and smooth fine motion. Moreover, the entire heightthereof is low, the stiffness of the motion stage itself is high, andthe system is little influenced by a change or gradient of temperature.

1. An ultra-precision positioning system, comprising: a base; a motionstage movably provided above a top of the base; a first feeding meansincluding a first actuator and first and second hinge elements with acircular hinge, the first feeding means performing an x-axistranslational motion of the motion stage with respect to the base; asecond feeding means including a second actuator and first and secondhinge elements with a circular hinge, the second feeding meansperforming a y-axis translational motion and a z-axis rotational motionof the motion stage with respect to the base; a third feeding meansincluding a third actuator and first and second hinge elements with acircular hinge, the third feeding means performing the y-axistranslational motion and the z-axis rotational motion of the motionstage with respect to the base in cooperation with the second feedingmeans; a fourth feeding means including a fourth actuator, first andsecond hinge members with a circular hinge, a first lever membercooperating with the second hinge member, and a third hinge membercooperating with the first hinge member, the fourth feeding meansperforming an x-axis rotational motion of the motion stage with respectto the base; and a control means for controlling the first to fourthactuators of the first to fourth feeding means.
 2. The system as claimedin claim 1, further comprising a fifth feeding means including a fifthactuator controlled by the control means, fourth and fifth hinge memberswith a circular hinge, a second lever member cooperating with the fifthhinge member, and a sixth hinge member cooperating with the second levermember, the fifth feeding means performing the x-axis rotational motionand a y-axis rotational motion of the motion stage with respect to thebase in cooperation with the fourth feeding means.
 3. The system asclaimed in claim 2, further comprising a sixth feeding means including asixth actuator controlled by the control means, seventh and eighth hingemembers with a circular hinge, a third lever member cooperating with theeighth hinge member, and a ninth hinge member cooperating with the thirdlever member, the sixth feeding means performing a z-axis translationalmotion, the x-axis rotational motion and the y-axis rotational motion ofthe motion stage with respect to the base in cooperation with the fourthand fifth feeding means.
 4. The system as claimed in claim 3, whereinthe second hinge member of the fourth feeding means, the fifth hingemember of the fifth feeding means and the eighth hinge member of thesixth feeding means penetrate through and are fitted into the thirdhinge member, the sixth hinge member and the ninth hinge member,respectively; and the first, second and third lever members are formedwith notch hinges and fixedly mounted with the second and third hingemembers, the fifth and sixth hinge members, and the eighth and ninthhinge members, respectively.
 5. The system as claimed in claim 3,wherein the first, fourth and seventh hinge members of the fourth tosixth feeding means are fixed to the base, respectively; the fourthfeeding means is arranged above and parallel to an x-axis centerline ofthe base; a center of the hinge of the second hinge member of the fourthfeeding means lies on a y-axis centerline of the base; and the fifth andsixth feeding means are arranged below and parallel to the x-axiscenterline of the base and to be symmetric with each other with respectto the y-axis centerline.
 6. The system as claimed in claim 3, whereinthe fourth to sixth feeding means are constructed to satisfy a followingrelationship equation:b=2a where a is a vertical distance between extensions of centers ofhinges of the second, fifth and eighth hinge members in an x-axisdirection and centers of the hinges of the first to third lever members,and b is a horizontal distance between extensions of centers of thehinges of the third, sixth and ninth hinge members in a y-axis directionand the centers of the hinges of the first to third lever members. 7.The system as claimed in claim 1, wherein the first and second hingeelements of the first feeding means are aligned with an x-axiscenterline of the base and fixed to the base and the motion stage,respectively; and a center of the hinge of the second hinge element ofthe first feeding means which is positioned on a side to be fixed to themotion stage is coincident with a center of the motion stage.
 8. Thesystem as claimed in claim 1, wherein the first and second hingeelements of the second and third feeding means are arranged parallel toa y-axis centerline of the base and fixed to the base and the motionstage, respectively; and centers of the hinges of the second hingeelements of the second and third feeding means which are positioned on aside to be fixed to the motion stage lie on an x-axis centerline of thebase.
 9. The system as claimed in claim 1, wherein a distance L betweenthe second and third feeding means satisfies a following relationshipequation: $L = \sqrt{\frac{2I}{m}}$ where m is mass of the motion stage,and I is mass moment of inertia of the motion stage.